%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP453-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:34:15 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 69 unt; 4 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 119 ( 119 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : inverse(A) = divide(divide(B,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X0),divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f9,definition,
sF1_fnc = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f10,definition,
sF0_fnc = multiply(sF1_fnc,c3),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f11,definition,
sF3_fnc = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f12,definition,
sF2_fnc = multiply(a3,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f13,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f8,f12,f11,f10,f9]) ).
fof(f345,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f348,plain,
! [X0,X1] : inverse(X0) = divide(inverse(divide(X1,X1)),X0),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f361,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f7,f345]) ).
fof(f363,plain,
! [X0,X1] : inverse(X0) = divide(multiply(inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f345,f7]) ).
fof(f368,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(divide(X1,X1)),X0),
inference(paramodulation,[status(thm)],[f345,f348]) ).
fof(f373,plain,
! [X0,X1] : inverse(X0) = divide(inverse(multiply(inverse(X1),X1)),X0),
inference(paramodulation,[status(thm)],[f345,f348]) ).
fof(f422,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f7,f5]) ).
fof(f423,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f7,f422]) ).
fof(f424,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,divide(X1,divide(inverse(X0),inverse(X2))))),X2) = X1,
inference(paramodulation,[status(thm)],[f345,f423]) ).
fof(f425,plain,
! [X0,X1,X2] : divide(inverse(inverse(divide(X0,divide(inverse(multiply(inverse(X1),X1)),X2)))),X2) = X0,
inference(paramodulation,[status(thm)],[f363,f423]) ).
fof(f433,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(X0,X1)),X2) = inverse(divide(X3,divide(X1,divide(inverse(X3),divide(inverse(X0),X2))))),
inference(paramodulation,[status(thm)],[f423,f423]) ).
fof(f435,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,inverse(divide(inverse(X0),X1)))),X1) = divide(X2,X2),
inference(paramodulation,[status(thm)],[f7,f423]) ).
fof(f442,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,divide(X1,multiply(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f345,f424]) ).
fof(f443,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,inverse(X1)))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f373,f425]) ).
fof(f444,plain,
! [X0,X1] : divide(inverse(inverse(multiply(X0,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f345,f443]) ).
fof(f453,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,divide(inverse(X0),X1))),X1) = divide(X2,X2),
inference(forward_demodulation,[status(thm)],[f345,f435]) ).
fof(f468,plain,
divide(inverse(inverse(sF0_fnc)),c3) = sF1_fnc,
inference(paramodulation,[status(thm)],[f10,f444]) ).
fof(f504,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f453,f453]) ).
fof(f513,plain,
! [X0] : divide(inverse(multiply(inverse(sF0_fnc),sF1_fnc)),c3) = divide(X0,X0),
inference(paramodulation,[status(thm)],[f468,f453]) ).
fof(f561,plain,
! [X0,X1] : inverse(divide(X0,X0)) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f7,f504]) ).
fof(f880,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(X0,divide(inverse(X1),divide(inverse(X0),X2)))),X2) = inverse(divide(X1,inverse(divide(X3,X3)))),
inference(paramodulation,[status(thm)],[f561,f433]) ).
fof(f881,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(X0,divide(inverse(X1),divide(inverse(X0),X2)))),X2) = inverse(divide(X1,divide(X3,X3))),
inference(paramodulation,[status(thm)],[f504,f433]) ).
fof(f948,plain,
! [X0,X1] : inverse(X0) = inverse(divide(X0,inverse(divide(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f423,f880]) ).
fof(f949,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(X0,divide(X1,X1))),
inference(forward_demodulation,[status(thm)],[f345,f948]) ).
fof(f950,plain,
! [X0,X1] : inverse(X0) = inverse(divide(X0,divide(X1,X1))),
inference(forward_demodulation,[status(thm)],[f423,f881]) ).
fof(f1856,plain,
! [X0,X1] : divide(inverse(inverse(X0)),divide(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f949,f444]) ).
fof(f1885,plain,
! [X0,X1] : inverse(inverse(inverse(multiply(X0,divide(X1,X1))))) = inverse(X0),
inference(paramodulation,[status(thm)],[f444,f950]) ).
fof(f1952,plain,
! [X0] : inverse(inverse(inverse(X0))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f949,f1885]) ).
fof(f2006,plain,
! [X0,X1] : X0 = multiply(X0,divide(X1,X1)),
inference(paramodulation,[status(thm)],[f444,f1856]) ).
fof(f2010,plain,
! [X0,X1] : divide(inverse(inverse(X0)),divide(X1,X1)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f1952,f1856]) ).
fof(f2055,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f1856,f2010]) ).
fof(f2092,plain,
! [X0,X1] : X0 = multiply(inverse(divide(X1,X1)),X0),
inference(backward_demodulation,[status(thm)],[f2055,f368]) ).
fof(f2093,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = X1,
inference(backward_demodulation,[status(thm)],[f2055,f361]) ).
fof(f2124,plain,
! [X0,X1,X2] : inverse(divide(X0,divide(X1,multiply(inverse(X0),divide(X2,X2))))) = X1,
inference(paramodulation,[status(thm)],[f442,f2006]) ).
fof(f2154,plain,
! [X0,X1] : inverse(divide(X0,divide(X1,inverse(X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f2006,f2124]) ).
fof(f2155,plain,
! [X0,X1] : inverse(divide(X0,multiply(X1,X0))) = X1,
inference(forward_demodulation,[status(thm)],[f345,f2154]) ).
fof(f2628,plain,
! [X0,X1,X2] : multiply(inverse(divide(divide(X0,X0),divide(X1,X2))),X2) = X1,
inference(paramodulation,[status(thm)],[f2092,f442]) ).
fof(f2640,plain,
! [X0,X1] : multiply(inverse(inverse(divide(X0,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f7,f2628]) ).
fof(f2641,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f2055,f2640]) ).
fof(f2713,plain,
! [X0] : multiply(divide(X0,X0),c3) = inverse(multiply(inverse(sF0_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f513,f2641]) ).
fof(f2744,plain,
c3 = inverse(multiply(inverse(sF0_fnc),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f2093,f2713]) ).
fof(f2756,plain,
! [X0,X1] : inverse(divide(X0,X1)) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f2641,f2155]) ).
fof(f3481,plain,
! [X0,X1,X2] : divide(divide(divide(X0,divide(inverse(X1),X2)),X1),X2) = X0,
inference(backward_demodulation,[status(thm)],[f2756,f423]) ).
fof(f3507,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f345,f2756]) ).
fof(f4546,plain,
multiply(inverse(sF0_fnc),sF1_fnc) = inverse(c3),
inference(paramodulation,[status(thm)],[f2744,f2055]) ).
fof(f4881,plain,
! [X0,X1,X2] : divide(divide(divide(X0,inverse(multiply(X1,X2))),X2),X1) = X0,
inference(backward_demodulation,[status(thm)],[f3507,f3481]) ).
fof(f4921,plain,
! [X0,X1,X2] : divide(divide(multiply(X0,multiply(X1,X2)),X2),X1) = X0,
inference(forward_demodulation,[status(thm)],[f345,f4881]) ).
fof(f4970,plain,
! [X0] : divide(divide(multiply(X0,sF1_fnc),b3),a3) = X0,
inference(paramodulation,[status(thm)],[f9,f4921]) ).
fof(f5913,plain,
divide(divide(inverse(c3),b3),a3) = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f4546,f4970]) ).
fof(f5930,plain,
divide(inverse(multiply(b3,c3)),a3) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f3507,f5913]) ).
fof(f5931,plain,
inverse(multiply(a3,multiply(b3,c3))) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f3507,f5930]) ).
fof(f5932,plain,
inverse(multiply(a3,sF3_fnc)) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f11,f5931]) ).
fof(f5933,plain,
inverse(sF2_fnc) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f12,f5932]) ).
fof(f5956,plain,
sF0_fnc = inverse(inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f5933,f2055]) ).
fof(f5965,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f2055,f5956]) ).
fof(f5966,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5965,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP453-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:15:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.15/0.49 % Refutation found
% 0.15/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.51 % Elapsed time: 0.125063 seconds
% 0.15/0.51 % CPU time: 0.843357 seconds
% 0.15/0.51 % Total memory used: 25.713 MB
% 0.15/0.51 % Net memory used: 24.592 MB
%------------------------------------------------------------------------------